CogAT Quantitative Battery: Number Series, Analogies & Puzzles Explained
April 12, 2026 · 7 min read
Parents often assume the quantitative battery is about math skills — multiplication tables, fractions, or arithmetic speed. It isn't. It tests mathematical reasoning: the ability to see patterns in numbers and relationships between quantities.
A child who is average at school math can excel here. A child who is excellent at arithmetic but hasn't practiced pattern recognition can struggle. The good news: these reasoning skills respond quickly to targeted practice.
The Three Question Types
1. Number Series
A sequence of numbers follows a rule. One number is missing. Your child must find the rule and identify the missing number.
Examples by difficulty:
Easy: 2, 4, 6, 8, ___ → 10 (count by 2s)
Medium: 3, 5, 8, 12, 17, ___ → 23 (differences increase by 1: +2, +3, +4, +5, +6)
Hard: 1, 1, 2, 3, 5, 8, ___ → 13 (Fibonacci: each = sum of two before it)
Strategy: Calculate the differences between consecutive terms first. If the differences themselves form a pattern (increasing, decreasing, constant), that is the rule. If not, look for multiplication or division relationships.
2. Number Analogies
Like verbal analogies, but with numbers. A relationship exists between the first pair of numbers. Your child applies the same relationship to complete the second pair.
Examples:
Easy: 3 is to 6 as 7 is to ___ → 14 (×2)
Medium: 4 is to 16 as 3 is to ___ → 9 (squared)
Hard: 16 is to 4 as 81 is to ___ → 9 (square root)
Common operations: doubling, halving, squaring, square roots, adding/subtracting a fixed amount, percentage relationships. At grade 5, more complex relationships appear.
3. Number Puzzles
A mathematical problem presented as a word problem or equation with a missing value. These range from simple missing-value equations to multi-step word problems requiring logical setup.
Examples:
Simple: If □ + 3 = 7, what is □? → 4
Word problem: Anna has twice as many stickers as Ben. Together they have 24. How many does Anna have? → 16
Ratio: The ratio of boys to girls is 3:2. There are 30 students. How many are girls? → 12
What This Battery Is Really Testing
All three question types test the same underlying skill: seeing structure in numbers. Children who naturally notice "hey, each number is double the last one" or "the differences are 1, 2, 3, 4..." have an advantage. That noticing is a habit of mind that can be developed.
Practice Tips
- Always calculate differences first on number series questions — it's the most reliable first step.
- Name the operation in analogies before picking an answer: "I think this is squaring" — then verify.
- For word problems, draw a simple diagram or write a short equation before calculating. Setup is half the battle.
- Don't avoid difficult questions. A hard number series question with a clear explanation is worth more than 5 easy ones.